Police said human bones were spotted by a helicopter pilot on the north face of the Matterhorn in August 2013.
A police team recovered the remains and equipment including an ice-axe.
They checked them against a database of some 280 climbers listed as missing in the region since 1926.
Thanks to DNA tests, experts have finally be able to identify the remains as those of an Englishmen who went missing in December 1979.
Police declined to reveal the 27-year-old man's name, citing Swiss confidentiality rules.
But as Alpine glaciers melt due to global warming, the remains of long-lost climbers have increasingly emerged from the shrinking mountain ice.